The mean value of a collection of values is equal to the ratio of the sum of the number of values in the set to the total number of values in the set. The expression of the central value of a set of data is the average of a list of data. It is defined mathematically as the ratio of the total of all the data to the number of units in the list. The average of a set of numerical data is also known as the mean in statistics. The average of two, three, and four equals (2+3+4)/3 = 9/3 = 3. As a result, 3 is the middle value of 2,3, and 4.
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The definition of average is to determine the mean value of a set of values.You can also check ,
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What is the formula for calculating average?
Average = Sum of Values/Number of Values
For a given collection of variables, we can easily determine the average. All we have to do now is add all of the values together and divide the result by the number of supplied values. Three simple procedures may be used to determine the average. They are as follows:
Finding the sum of all the provided numbers is the first step in calculating the average of numbers.
Step 2: Count the number of observations made:
The next step is to count the number of numbers in the dataset.
Step 3: Calculate the Average:
The average is then calculated by dividing the total by the number of observations.
Questions and answers
Question 1:
Five years ago the average age of husband and wife was 23 years. Today the average age of husband, wife and child is 20 years. How old is the child ?
Option 1: 4 years
Option 2: 5 years
Option 3: 3 years
Option 4: 4.5 years
Answer: 1: 4 years
Explanation:
Question 2
A cricketer whose bowling average is 12.4 runs per wicket, takes 5 wicket for 26 runs and there by improves his average by 0.4. The number of wickets taken by him till the past match was :
Option 1: 95
Option 2: 70
Option 3: 90
Option 4: 85
Answer: 3: 90
Explanation:
Question 3
A batman has an average of 30 runs in his 42 innings. The difference between his maximum and minimum score is 100. If these two innings are removed his average for 40 innings comes down to 28. What is his maximum score?
Option 1: 120
Option 2: 130
Option 3: 140
Option 4: 110
Answer: 1: 120
Explanation:
Question 4
The average of marks of 14 students was calculated as 71. But it was later found that the marks of two students had been wrongly entered as 42 instead of 56 and of another as 74 instead of 32. The correct average is :
Option 1: 67
Option 2: 68
Option 3: 69
Option 4: 71
Answer: 3: 69
Explanation:
Question 5
The average salary of all the associates in a team is Rs. 16000. The average salary of 7 senior associates is Rs. 24000 and the average salary of the rest is 12000. How many associates work in that team?
Option 1: 21
Option 2: 22
Option 3: 23
Option 4: 24
Answer: 1: 21
Explanation:
Question 6
The average monthly salary of the workers in a workshop is Rs. 8500. If the average monthly salary of 7 technicians is Rs. 10000 and average monthly salary of the rest is Rs. 7800, the total number of workers in the workshop is :
Option 1: 18
Option 2: 20
Option 3: 22
Option 4: 24
Answer: 3: 22
Explanation:
Question 7
The average salary of all the workers in a workshop is Rs. 8000. The average salary of 7 technicians is Rs. 12000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is :
Option 1: 14
Option 2: 21
Option 3: 7
Option 4: 28
Answer: 2: 21
Explanation:
Question 8
The average salary of all the workers in a workshop is Rs. 8000. The average salary of 7 technicians is Rs. 12000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is :
Option 1: 14
Option 2: 21
Option 3: 7
Option 4: 28
Answer: 2: 21
Explanation:
Applying Alligation
12000 5000
10000
5000 2000
Ratio = 5 : 2
If 5 === 20
then 2 === 8
Question 9
The average monthly salary of all the employees in an industry is Rs. 12000. The average salary of male employees is Rs. 15000 and that of female employees is Rs. 8000. What is the ratio of male employees to female employees?
Option 1: 4:5
Option 2: 3:4
Option 3: 4:3
Option 4: 3:5
Answer: 3: 4:3
Explanation:
Question 10
The average age of 5 boys is 12 years. The average age of 3 others is 16 years. The average ageofallthe8boysis:
Option 1: 13 12 years
Option 2: 14 years
Option 3: 1212 years
Option 4: 13 years
Answer: 1: 1312 years/
Explanation:
Question 11
In a school the average age of students is 6 years and the average age of 12 teachers is 40 years. If average age of combined group of all the teachers and students is 7 years, then the number of students is :
Option 1: 396
Option 2: 400
Option 3: 496
Option 4: 398
Answer: 1: 396
Explanation:
Question 12
The average of marks obtained by 120 candidates in a certain examination is 35. If the average marks obtained by passed candidates are 39 and those of the failed candidates are 15, what is the number of candidates who passed the examination?
Option 1: 100
Option 2: 200
Option 3: 150
Option 4: 140
Answer: 1: 100
Explanation:
Question 13
The average marks of 100 students were found to be 40. Later on it was discovered that a score of 53 was misread as 83. Find the correct average corresponding to the correct score.
Option 1: 38.7
Option 2: 39
Option 3: 39.7
Option 4: 41
Answer: 3: 39.7
Explanation:
Question 14:
The average salary, per head of all the workers of the institution is Rs. 60. The average salary of 12 officer Rs. 400, the average salary, per head of the rest is Rs. 56 .The total number of workers in the institution is :
Option 1: 1000
Option 2: 1012
Option 3: 1032
Option 4: 1020
Answer: 3: 1032
Explanation:
Question 15:
The average high temperature from Mon to Wed is 37 C while the average temperature from Tue to Thursday is 34 C. The temperature of Thursday is ⅘ times that of Mon. Find the temperature of Thursday.
Option 1: 32 C
Option 2: 35 C
Option 3: 36 C
Option 4: 33 C
Answer: 3: 36C
Explanation:
Question 16:
In my class, the average age of 29 boys is 15 years. But by mistake, my friend, aged 20 years, was counted twice and two boys were missed in that count, whose ages differ by 5 years. If even after correction, the average age of all boys in the class remains 15 years, the age of the younger boy, who was missed in counting, is
Option 1: 20 years
Option 2: 15 years
Option 3: 10 years
Option 4: 18 years
Answer: 2: 15 years
Explanation:
Given that, average age of 29 boys is 15 years. But by mistake, my friend, aged 20 years, counted twice and two boys were missed in that count, whose ages differ by 5 years.
Average age of n persons = (Sum of age of n persons)/(Number of persons)
⇒ Incorrect sum of ages of 29 boys = Average age of 29 boys × 29
⇒ Incorrect sum of ages of 29 boys = 15 × 29 = 435 years
Since one boy, of age 20 years, was counted twice,
Sum of 28 boys = 435 – 20 = 415 years.
Now, let the age of younger boy among the two, who were missed in counting be x years and that of the older
boy is (x + 5) years.
⇒ Correct sum of ages of boys of the class = 415 + x + (x + 5) = 420 + 2x
Since, average age of the boys of the class, after correction is still 15 years, so
Average age of 30 boys = (420 + 2x)/30
⇒ (420 + 2x)/30 = 15
⇒ 420 + 2x = 15 × 30
⇒ 420 + 2x = 450
⇒ 2x = 450 – 420 = 30
⇒ x = 30/2
⇒ x = 15 years
Question 17:
The average age of 29 students and the principal is 17 years. The average age decreases by 1 year when the principal’s age is not considered. What is the age of the principal?
Option 1: 38 years
Option 2: 40 years
Option 3: 46 years
Option 4: 37 years
Answer:
3: 46 years
Explanation:
According to the given information,
Let assume the sum of age of 29 students is ∑S and the age of principal be P.
We know that, Average = Sum of all observations/Number of observations
Average age of 29 students and principal = 17
Here, total number of people = 30
And sum of ages of 29 students and Principal = P + ∑S
∴ 17 = (P + ∑S)/30
⇒ P + ∑S = 17 × 30 = 510
Now, Average age of 29 students = 17 – 1 = 16
16 = ∑S/29
∑S = 29 × 16 = 464
P = (P + ∑S) – ∑S = 510 – 464 = 46 years
Question 18:
In the following question, two statements are numbered as A and B. On solving these statements we get quantities A and B respectively. Solve for the both quantities and chose the correct option.
Quantity A: A team of 6 persons joins in a swimming competition. The best swimmer score 72 point. If he had scored 88 points, the average of score for the team would have been 75. The number of points team scored was .... Quantity B: The average of 7 consecutive positive integers is 32. The product of the largest and smallest integer is ..
Option 1: Quantity A > Quantity B
Option 2: Quantity A < Quantity B
Option 3: Quantity A ≥ Quantity B
Option 4: Quantity A ≤ Quantity B
Answer: 2:Quantity A < Quantity B
Explanation:
Solving for Quantity A:
Number of person in team = 6
Let assume sum of score done by 5 person = x
Average of score done by team = 75 only if swimmer score 88 points
Sum of score done by team = x + 88
Average = Sum of score/number of team member
⇒ 75 = (x + 88)/6
⇒ 450 = x + 88
⇒ x = 450 - 88 = 362
So, Actual total score by team = 362 + 72 = 434
Solving for Quantity B:
Average value = 32
Number of quantity = 7
Let assume first number x,
Due to consecutive number,
Second number = x + 1;
Third number = x + 2;
Fourth number = x + 3;
Fifth number = x + 4;
Sixth number = x + 5;
Seventh number = x + 6;
Sum of Quantity = 32 × 7 = 224
⇒ x + x + 1 + x + 2 + x + 3 + x + 4 + x + 5 + x + 6 = 224
⇒ 7x + 21 = 224
⇒ 7x = 203
⇒ x = 29
Smallest number = 29
Largest number = x + 6 = 29 + 6 = 35
Product = 29 × 35 = 1015
∴ Quantity A < Quantity B
Question 19:
In the following question, two statements are numbered as A and B. On solving these statements we get quantities A and B respectively. Solve for the both quantities and choose the correct option.
Quantity A: The average of a group of 9 numbers is 115. When a number is added to the group, the new average is 27 more than the number. Find the number.
Quantity B: The average of a series of 8 numbers is 96. When two numbers are added to the series, the average is reduced by 3. If the difference between the numbers is 8, find the numbers.
Option 1: Quantity A > Quantity B
Option 2: Quantity A < Quantity B
Option 3: Quantity A ≥ Quantity B
Option 4: Quantity A ≤ Quantity B
Answer: 3: Quantity A ≥ Quantity B\
Explanation:
Solving for Quantity A:
Let the number be ‘x’
Sum of 9 numbers = 9 × 115 = 1035
When the number is added, sum of 10 numbers = 1035 + x
Average of 10 numbers = 27 + x
⇒ 10(27 + x) = 1035 + x
⇒ 270 + 10x = 1035 + x
⇒ 9x = 765
⇒ x = 765/9 = 85
⇒ Quantity A = 85
Solving for Quantity B:
Let the numbers be ‘x’ and ‘(x + 8)’
Sum of 8 numbers = 8 × 96 = 768
Sum of 10 numbers = 768 + x + x + 8 = 776 + 2x
Average of 10 numbers = 96 - 3 = 93
⇒ 776 + 2x = 10(93)
⇒ 2x = 930 - 776
⇒ x = 154/2 = 77
⇒ x + 8 = 77 + 8 = 85
⇒ Quantity B = 77, 85
∴ Quantity A ≥ Quantity B
Question 20:
Weight of a student is wrongly measured as 84 instead of 48. Therefore, average weight of class students got increased by 0.5 kg. What is the class strength?
Option 1: 56
Option 2: 60
Option 3: 64
Option 4: 72
Answer: 4: 72
Explanation:
When weight of student is wrongly recorded as 84 instead of 48 the average of weight of class increased by 0.5 kg.
Let the strength of class be X.
Total increased in weight = 0.5 × X = 0.5X ----(1)
This increased in weight statistics is equal to difference between actual and misreported weight of student.
Increase in weight = 84 - 48 = 36 kg ----(2)
Equating results (1) & (2) -
0.5X = 36 (∵ X - 0.5X =0.5X)
⇒ X = 72
